求x^1/x当x趋于正无穷是的极限

题目

求x^1/x当x趋于正无穷是的极限
x^(1/x)

答案

lim(x→+∞) x^(1/x)
=lim(x→+∞) e^[lnx^(1/x)]
=lim(x→+∞) e^(lnx/x)
=e^[lim(x→+∞) (lnx/x)]
=e^[lim(x→+∞) (1/x)]
=e^0
=1